I was wondering if it was possible to mount objectives of different brands and different types on a microscope.
EX. Leica with 10x Nikon plan infinity objective and 20X Zeiss infinity non-plan objective.
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As I understand it, the main advantage of infinity is the ability to add extra equipment between the head and objective without having to add extra optics to correct the focal point; beamsplitters, analyzers, whatever you've got, because the eyepiece doesn't have to be at a set distance from the objective. Also adding extra equipment shouldn't significantly alter the magnification.
Infinity is not necessarily better than finite. There have been very high end finite optics. Today all high-end microscopes use infinite optics while low end Chinese stuff is frequently finite. That may give the false impression that infinite is always better.
My speculations, if I'm wrong please inform otherwise....
Another take - "necessity" is supposedly the mother of invention. The primary advantage of infinity designs is allowing the insertion of additional imaging elements (beam splitters, DIC prisms, Bertrand lenses, etc.) between the objective and eyepiece. Prior to the 1930's when Reichert pioneered infinity compound microscopes, there wasn't much call for epi-flluorescence, DIC was decades away, and phase contrast had just been invented.
American Optical bought Spencer Lens Co. a few years prior to 1935. 1931 or 32.